1. Field of the Invention
The invention relates to characterization of dispersed particles, e.g., determination of particle size distribution.
2. Discussion of the Related Art
Processes such as chemical-mechanical planarization (CMP) and sol-gel fabrication of silica bodies utilize dispersions of particles in a liquid medium. (For a discussion of CMP and sol-gel processes, see, respectively, P. Van Zant, Microchip Fabrication, 3rd Ed., McGraw-Hill, 300 (1997), and U.S. Pat. No. 5,240,488.) For such processes, it is desirable to know the specific properties of the particles. For example, larger particles in CMP often lead to scratches and variations in the median particle size and the size distribution sometimes lead to inconsistent polishing. Similarly, the properties of sol-gel derived bodies depend in large part on the characteristics of the particles in the dispersion. For these reasons, among others, various methods have been developed to determine the characteristics of particles in such dispersions.
One such characteristic is the particle size distribution (PSD). See, for example, U.S. Pat. Nos. 4,706,509, 5,121,629, and 5,569,844 (the '509, '629, and '844 patents, respectively). The '509 patent relates to a method for ultrasonically measuring solids concentration and particle size distribution in a dispersion. Ultrasonic waves at a variety of frequencies are directed into the dispersion, and the attenuation at the frequencies is measured. A dimensional spectrum (across the range of particle dimensions) is divided into dimensional intervals, and a system of linear equations is developed to represent the concentration of particles in each dimension interval. The system of equations is then solved to determine the PSD. However, the process of the '509 patent is limited to waves having a wavelength smaller than the largest particles. The process is therefore not useful for relatively fine particles, e.g., tens to hundreds of nanometers, since acoustic waves cannot presently be driven at the necessary frequencies.
The process of the '844 patent involves measuring the attenuation of both ultrasonic waves and electromagnetic radiation to determine particle size distribution. Specifically, ultrasonic velocity and ultrasonic attenuation are combined with the density, as determined from the electromagnetic radiation attenuation, to calculate the PSD. In addition to the problems inherent in generating x-rays or gamma rays, however, particle sizes of about 10 to 15 .mu.m appear to be the lower limit for the process.
In the '629 patent, the disclosure of which is hereby incorporated by reference, ultrasonic waves at a variety of selected wavelengths are passed through a dispersion, and the attenuation at each frequency is measured to derive a measured attenuation spectrum over those frequencies. Separately, based on a theoretical model, a set of attenuation spectra are calculated for a variety of PSDs, and the calculated spectra are then compared to the measured spectrum to formulate a preliminary approximation of the PSD of the dispersion. Further calculations must be performed, starting from this approximation, to more accurately determine the PSD.
While current techniques for characterizing dispersed particles, e.g., determining PSD, are adequate for many purposes, improvements that provide more accurate, consistent, and reliable results are desired.